Boost Your Pre-Algebra Skills with Examples and Solutions

High School
Algebra
Pre-Algebra

(a) How do we express a rational function r as a partial frac- tion decomposition?
(b) Give the form of the partial fraction decomposition.
$(i) \frac{2 x}{(x - 5) {(x - 1)}^{2}}$
$(i i) \frac{2 x}{(x - 5) (x^{2} + 1)}$
$(i i i) \frac{3 x + 1}{x {(x^{2} + 1)}^{2}}$

Dolly Robinson 2021-10-10

Decompose the fraction into partial fractions.
a) $\frac{x^{2}}{{(x - 1)}^{3}} = ?$
b) $\frac{x^{2} - 7 x + 3}{x^{3} - 2 x^{2} + x} = ?$
c) $\frac{4 x^{2}}{+} 7 x + 4} {x {(x + 1)}^{2}} = ?$
d) $\frac{4 x^{2} + x + 6}{x^{3} + 2 x} = ?$

sjeikdom0 2021-10-10

Simplify the expression
$4 + \frac{2}{u} - \frac{3 u}{u + 5}$

preprekomW 2021-10-10

Which step has the error? Describe what the error is
$\frac{5 r^{2}}{2 r + 3} \div \frac{4 r + 6}{10}$
Step 1: $\frac{5 r^{2}}{2 r + 3} \times \frac{2 (2 r + 3)}{10}$
Step 2: $\frac{5 r^{2}}{1} \times \frac{2}{10} = \frac{10 r^{2}}{10}$
Step 3: $\frac{10 r^{2}}{10} = r^{2}$

Jason Farmer 2021-10-09

The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm , find the dimensions of the poster with the smallest area.

tinfoQ 2021-10-09

Prove that for every n in the set of natural numbers, N:
$\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \dots + \frac{1}{(2 n - 1) \cdot (2 n + 1)} = \frac{n}{2 n + 1}$

SchachtN 2021-10-09

To explain:
The statement "The techniques used for solving linear equations and linear inequalities are similar, yet different".

FizeauV 2021-10-09

$\sum_{n = 1}^{8} (3 n - 4)$
1) Campfire Mocha
2) -1
3) 76
4) 20

Ayaana Buck 2021-10-08

Solve by the method of elimination.
1. $x - 3 y = 2$
$2 x + 3 y = 13$
2. $3 x + 10 y = 2$
$x - 2 y = - 6$
3. $3 x + 2 y = 12$
$3 x - y = 3$

Yulia 2021-10-08

How many permutations of the letters ABCDEFG contain the string BCD?

Jason Farmer 2021-10-08

For exercise, solve the equations and inequalities. Write the solutions sets to the inequalities in interval notation if possible.
$\frac{- 5 x {(x - 3)}^{2}}{2 + x} \leq 0$

x f(x) 0 0 2 396 4 1605 6 3597 8 6403 10 10008

beljuA 2021-10-04

write the ratio as a fraction in lowest terms.
$2 \frac{3}{4} to 1 \frac{1}{2}$
$2 \frac{3}{4} is___ % of 1 \frac{1}{2}$

smileycellist2 2021-10-04

My car gets 28 miles per gallon, and gasoline costs $2.90 per gallon. If we consider only the cost of gasoline, how much does it cost (in dollars) to drive each mile? Round your answer to the nearest cent.
Choose the TWO fractions that are multiplied together to calculate the solution using dimensional analysis. Make sure that the units of the fractions you choose cross-cancel to produce the unit of your desired answer. You must have the correct two fractions selected at the same time to get credit when you check your answer. You get two attempts to check your answer.
$\begin{array}{cc} 1 g a l l o n & 2.90 d o l l a r s \\ 28 m i l e s & 1 g a l l o n \\ 1 g a l l o n & 28 m i l e s \\ 2.90 d o l l a r s & 1 g a l l o n \end{array}$
If we consider only the cost of gasoline, how much does it cost (in dollars) to drive each mile? Round your answer to the nearest cent.
$ per mile

vazelinahS 2021-10-04

$\frac{10}{20}$ and $\frac{1}{15}$ are fractions. let x be the another fraction.when the fraction x is multiplied by $\frac{10}{20}$ and then added with $\frac{1}{15}$ the resultant fraction is $\frac{8}{6}$ . Find the value of the fraction x ?

Caelan 2021-10-04

Mary cut a piece of yarn that is $\frac{9}{5}$ feet long into 3 pieces. List 3 different fractions that could show the length of the 3 fractions in ft.

babeeb0oL 2021-10-04

Tell whether the ratis form a proportion
$\frac{9}{4}, \frac{2}{3}$
a) Yes

b) No

zi2lalZ 2021-10-04

Express each of the following as a single fraction involving positive exponents only.
$3 a^{- 2} + 4 b^{- 1}$

Yasmin 2021-10-04

The length of a rectangle is 5m longer than its width. If the perimeter of the rectangle is 70m, find its length and width.
length: ?m
width: ?m

Dottie Parra 2021-10-04

For Exercise, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.
${(x^{2} - 9)}^{2} - 2 (x^{2} - 9) - 35 = 0$

Getting your pre Algebra solved becomes much easier when you have all the answers to your questions by taking a closer look at the various examples dealing with Pre-Algebra subjects. We have intentionally collected the list of pre-algebra equations and various solving equations with decimals problems to help you see various examples that explain how certain solutions are found. Still, if something sounds unclear or you are concerned about some solution that has been provided, approach pre-algebra with reverse engineering approach (going backwards).

Pre-Algebra

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